The radius of curvature of a concave mirror is 30 cm. Following Cartesian Sign Convention, its focal length is expressed as ________.

CONCEPT:

Concave mirror: 

• If the inner surface of the spherical mirror is the reflecting surface, then it is called a concave mirror. It is also called a focusing mirror/converging mirror.
• • The size of the image produced by these mirrors can be larger or smaller than the object, depending upon the distance of the object from the mirror.
  • The concave mirror can form both real as well as virtual images of any object.

Sign convention in mirrors

• All distance are measured from the pole of the mirror.
• The distance measured from the pole (p) to the left side of the mirror is taken as negative.
• The distance measured from the pole (p) to the right side of the mirror is taken as positive.
• The heights measured upwards and perpendicular to the principal axis of the mirror is taken as positive.
• The heights measured downwards and perpendicular to the principal axis of the mirror is taken as negative.

​EXPLANATION:

Given - Radius of curvature (R) = - 30 cm

• The relationship between the focal length (f) and the radius of curvature (R) is given by -

\(\Rightarrow f = \frac{R}{2}\)

\(\Rightarrow f = \frac{-30}{2}=-15 cm\)